# Package com.singularsys.extensions.polynomials

See: Description

• Interface Summary
Interface Description
PNodeI
An element in a polynomial representation of an expression.
• Class Summary
Class Description
AbstractPNode
Default methods, when more specific methods do not work.
Coeffs
Jep function to extract array of coefficients from a polynomial.
Compare
The `compare(x,y)` command.
Expand
The expand(x) command.
Monomial
Represents an immutable monomial a x^i * y^j * ... * z^k, a constant.
MutableMonomial
A mutable monomial representing a * x^i * y^j * ... * z^k.
MutablePolynomial
A mutable polynomial representing a + b + c.
PConstant
Represents a constant.
PFunction
Represents a function.
Polynomial
Represents a polynomial.
PolynomialCreator
A system for symbolic simplification, expansion and comparision based on conversion to a canonical polynomial representation.
POperator
Represents an operator.
PVariable
Represents a variable.
Simplify
The simplify(x) command.

## Package com.singularsys.extensions.polynomials Description

An advanced simplification/expansion/comparison algorithm. To use
```PolynomialCreator pc = new PolynomialCreator(jep);
Node simp = pc.simplify(node);
Node expand = pc.expand(node);
boolean flag = pc.equals(node1,node2);
int res = pc.compare(node1,node2);
PNodeI poly = pc.createPoly(node);
```

## How it works

The basic idea is to reduce each equation to a canonical form based on a total ordering of the terms. For example a polynomial in `x` will always be in the form `a+b x+c x^2+d x^3.` This makes comparison of two polynomials easy as it is just necessary to compare term by term, whereas it is dificult to compare `x^2-1` with `(x+1)*(x-1)` without any simplification or reordering is tricky.

As an illustration some of the rules for the ordering are `0<1<2`, `5<x`, `x<x^2<x^3`, `x<y`.

A polynomial is constructed from a set of monomials by arranging the monomials in order. Likewise a monomial is constructed from a set of variables by arranging the variables in name order.

The algorithm can also work with non-polynomial equations. Functions are order by the name of the function and the ordering of their arguments. Hence `cos(x)<sin(x)<sin(y)`.

Since:
Jep 3.5 / Extensions 2.0